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Register a new userQuantum Many-Body Scar States with Emergent Kinetic Constraints and Finite-Entanglement Revivals
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We construct a set of exact, highly excited eigenstates for a nonintegrable spin-1/2 model in one dimension that is relevant to experiments on Rydberg atoms in the antiblockade regime. These states provide a new solvable example of quantum many-body scars: their sub-volume-law entanglement and equal energy spacing allow for infinitely long-lived coherent oscillations of local observables following a suitable quantum quench. While previous works on scars have interpreted such oscillations in terms of the precession of an emergent macroscopic SU(2) spin, the present model evades this description due to a set of emergent kinetic constraints in the scarred eigenstates that are absent in the underlying Hamiltonian. We also analyze the set of initial states that give rise to periodic revivals, which persist as approximate revivals on a finite timescale when the underlying model is perturbed. Remarkably, a subset of these initial states coincides with the family of area-law entangled Rokhsar-Kivelson states shown by Lesanovsky to be exact ground states for a class of models relevant to experiments on Rydberg-blockaded atomic lattices.
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A quantum many-body scar system usually contains a special non-thermal subspace (approximately) decoupled from the rest of the Hilbert space. In this work, we propose a general structure called deformed symmetric spaces for the decoupled subspaces hosting quantum many-body scars, which are irreducible sectors of simple Lie groups transformed by matrix-product operators (or projected entangled pair operators), of which the entanglement entropies are proved to obey sub-volume-law scaling and thus violate the eigenstate thermalization hypothesis. A deformed symmetric space, in general, is required to have at least a U(1) sub-Lie-group symmetry to allow coherent periodic dynamics from certain low-entangled initial states. We enumerate several possible deforming transformations based on the sub-group symmetry requirement and recover many existing models whose scar states are not connected by symmetry. In particular, a two-dimensional scar model is proposed, which hosts a periodic dynamical trajectory on which all states are topologically ordered.
We find exponentially many exact quantum many-body scar states in a two-dimensional PXP model -- an effective model for a two-dimensional Rydberg atom array in the nearest-neighbor blockade regime. Such scar states are remarkably simple valence bond solids despite being at effectively infinite temperature, and thus strongly violate the eigenstate thermalization hypothesis. Given a particular boundary condition, such eigenstates have integer-valued energies. Moreover, certain charge-density-wave initial states give rise to strong oscillations in the Rydberg excitation density after a quantum quench and tower-like structures in their overlaps with eigenstates.
We show that the magnetization of a single `qubit spin weakly coupled to an otherwise isolated disordered spin chain exhibits periodic revivals in the localized regime, and retains an imprint of its initial magnetization at infinite time. We demonstrate that the revival rate is strongly suppressed upon adding interactions after a time scale corresponding to the onset of the dephasing that distinguishes many-body localized phases from Anderson insulators. In contrast, the ergodic phase acts as a bath for the qubit, with no revivals visible on the time scales studied. The suppression of quantum revivals of local observables provides a quantitative, experimentally observable alternative to entanglement growth as a measure of the `non-ergodic but dephasing nature of many-body localized systems.
We investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints. Using random unitary circuits, we compute ensemble-averaged spectral form factors and linear-response correlation functions, and find that their characteristic time scales are given by the inverse gap of an effective Hamiltonian$-$or equivalently, a transfer matrix describing a classical Markov process. Our approach allows us to connect directly the Thouless time, $t_{text{Th}}$, determined by the spectral form factor, to transport properties and linear response correlators. Using tensor network methods, we determine the dynamical exponent, $z$, for a number of constrained, conserving models. We find universality classes with diffusive, subdiffusive, quasilocalized, and localized dynamics, depending on the severity of the constraints. In particular, we show that quantum systems with Fredkin constraints exhibit anomalous transport with dynamical exponent $z simeq 8/3$.
Quantum many-body scar states are exceptional finite energy density eigenstates in an otherwise thermalizing system that do not satisfy the eigenstate thermalization hypothesis. We investigate the fate of exact many-body scar states under perturbations. At small system sizes, deformed scar states described by perturbation theory survive. However, we argue for their eventual thermalization in the thermodynamic limit from the finite-size scaling of the off-diagonal matrix elements. Nevertheless, we show numerically and analytically that the nonthermal properties of the scars survive for a parametrically long time in quench experiments. We present a rigorous argument that lower-bounds the thermalization time for any scar state as $t^{*} sim O(lambda^{-1/(1+d)})$, where $d$ is the spatial dimension of the system and $lambda$ is the perturbation strength.
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